Let fn(x)=xn be a real polynomial function where n is a non-negative integer.
a. (i) State the domain of fn.
b. (ii) Distinguish between the ranges of fn when n is even and when n is odd, giving each in interval notation.
c. (iii) Explain, with reasoning based on the symmetry of the graph, why the range identified in part (ii) is correct for even n.
d. (iv) Draw a rough sketch of y=fn(x) for n=2 and for n=3 on the same set of axes and indicate the portions of the y-axis that constitute their ranges.